Nonlinear eigenvalue problems arise in a variety of science and engineering applications,
and in the past ten years there have been numerous breakthroughs in the development of …

In this chapter we will consider the problem of computing all the zeros of an analytic function
1that lie in the interior of a Jordan curve"/. The algorithm that we will present computes not …

In this paper, we propose a method for finding certain eigenvalues of a generalized
eigenvalue problem that lie in a given domain of the complex plane. The proposed method …

We consider a Rayleigh-Ritz type eigensolver for finding a limited set of eigenvalues and
their corresponding eigenvectors in a certain region of generalized eigenvalue problems …

Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the n th
roots of unity. Based on these data, how can we approximately evaluate f(z) or f^(m)(z) at a …

Linear response theory, originally formulated for studying how near-equilibrium statistical
mechanical systems respond to small perturbations, has developed into a formidable set of …

In this chapter, we are primarily interested in the construction of computationally verifiable
initial conditions and the corresponding convergence analysis of the simultaneous methods …

Starting from a comparison of some established numerical algorithms for the computation of
the eigenvalues (discrete or solitonic spectrum) of the non-Hermitian version of the Zakharov …

For generalized eigenvalue problems, we consider computing all eigenvalues located in a
certain region and their corresponding eigenvectors. Recently, contour integral spectral …

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